Robust multi-class multi-period patient scheduling with wait time targets

Long wait times for health care services is a known challenge in most health care systems. This is partially due to limited capacity and increased demand, but also due to sub-optimal scheduling policies. In this paper, we consider a health system in which patients are prioritized based on their acuity level. We assume that there is a wait time target for each acuity level to ensure that patients of lower acuity do not wait for an unreasonable amount of time while higher acuity patients are being served. We apply a robust optimization (RO) approach to schedule patients over a multi-period finite horizon considering the wait targets. First, we present a deterministic mixed-integer programming model which considers patient priorities, available capacity, and wait time targets for each priority level. We then investigate the robust counterpart of the model by considering uncertainty in demand and employing the notion of budget of uncertainty. Finally, we numerically compare the proposed robust model with the deterministic method. Our results demonstrate that the proposed robust approach provides solutions with higher service levels and lower wait times. Our results also provide insights on how expanding capacity and choosing the level of uncertainty affect the performance of the system.